Dry rigid block masonry: Safe solutions in presence of Coulomb friction

Part of this paper refers to a research study developed by Jossa and the writer [1] now awaiting publication. It is well known that the static and kinematic behaviour of ancient dry block masonry structures is predominantly regulated by two parameters: self-weight and friction. And it is also well known that any investigation on the safety levels of these structures implies difficulties of analysis, due to the non-associated flow rules imposed by friction. Possibilities of non-unique solutions are directly consequent. This is, therefore, one of the main problems in every programme for the conservation and repair of such structures. The basic guideline of this research is to provide appropriate requirements to treat frictional materials within the framework of the standard limit analysis. This is possible, as shown in the paper, if a way to limit the space of statically admissible solutions can be defined in favour of safety. Generally, in classic plastic theory, an equilibrated distribution of internal forces gives a safe solution if the relative virtual work done, with reference to the true collapse configuration of the structure, is not greater than the virtual work done by the true force distribution. Therefore, in order to define a safe rigid-plastic model for frictional materials, a heuristic procedure to evaluate the minimum value of normal forces, with regard to the whole set of the statically admissible distributions, is herein proposed. Thus, a safe solution is obtainable with standard limit analysis by assuming the limiting frictional resistance to be that associated with this minimum normal force. The heuristic aspect of this procedure is particularly highlighted in the two case studies herein analysed: the 2D masonry wall subject to in-plane traction forces and the voussoir arch subject to its own weight.